JUDY WOODRUFF: Secretary of State John Kerry and his counterpart from Iran worked in Vienna today, trying to find a breakthrough in talks on Iran’s nuclear program. Kerry met one-on-one with Iranian Foreign Minister Mohammad Javad Zarif twice during the day for several hours. There was no indication of any real progress. The U.S. and five other nations are trying to reach an agreement with Tehran before a July 20 deadline.

A full audit of Afghanistan’s presidential runoff begins this week, under a deal brokered by Secretary Kerry over the weekend. Last month’s election was marred by allegations of fraud. Now the United Nations will oversee the review of some eight million ballots. The rival candidates, Abdullah Abdullah and Ashraf Ghani, have agreed to accept the outcome of the new count.

In Nigeria, a new video surfaced from the leader of the Boko Haram militants, the group that kidnapped 200 schoolgirls in April. In it, the group’s leader claims responsibility for attacks that the government never reported.

ABUBAKAR SHEKAU, Leader, Boko Haram (through interpreter): Refinery, yes, you people try to hide it. A woman sent by Allah bombed the refinery. You said it was an ordinary fire? A bomb exploded in Lagos. I ordered the bomb to be exploded, and you say it’s fire. If you hide it, you cannot hide from Allah.

JUDY WOODRUFF: The militant leader also mocked President Goodluck Jonathan and the outcry over the girls’ kidnapping. He offered again to trade them for fighters who are held in Nigerian jails.

The U.N. Security Council has approved sending humanitarian aid to parts of Syria held by rebels, even if the Syrian government objects. Today’s vote followed increasingly dire reports about the suffering of civilians. Currently, all aid has to go through Damascus, and the great majority winds up in government-controlled areas.

U.S. Army Sergeant Bowe Bergdahl returned to active duty today, after spending nearly five years as a Taliban prisoner in Afghanistan. He was assigned to administrative duties in San Antonio, Texas, where he’s had counseling and treatment for the past month. The Army is still investigating allegations that Bergdahl was captured after he deserted.

The wrecked Italian cruise liner Costa Concordia was painstakingly re-floated today off the Tuscan coast. The daylong operation took place more than two years after the vessel struck rocks and capsized, leaving 32 people dead.

Sally Biddulph of Independent Television News reports on today’s exercise.

SALLY BIDDULPH: With each passing hour, a few more cabins of the Costa Concordia are revealed. Almost imperceptibly, the huge vessel starts to float again in the biggest salvage operation in history.

Today, the ship is being slowly lifted from the manmade steel platform constructed beneath her by pumping air into the huge metal containers welded to her sides. She will then need to be fully checked before being towed by tugs to deeper water. There, under anchor, more air will be pumped into the containers to raise her to a fully floating position.

The luxury cruise liner went down off the coast of Tuscany two-and-a-half years ago. She’d sailed too close to the island of Giglio, where rocks ripped a hole in her hull; 32 people died in the ensuing chaos, as the ship capsized. The Concordia’s captain, Francesco Schettino, is currently on trial for what happened.

Until last September, the vessel rested unmoved on its side until salvage experts righted her in a huge engineering operation. The process to now float her is an even bigger challenge. Her final journey will be to the port of Genoa, where she will be stripped down and scrapped at the end of this month.

JUDY WOODRUFF: The ship’s captain is charged with manslaughter and with being among the first to abandon ship. He is, as you heard, currently on trial.

Breaking Foreign Secretary William Hague is stepping down after four years on the job. He announced this evening that he will become leader of the House of Commons. The surprise move is part of a cabinet reshuffle that conservative Prime Minister David Cameron plans to explain tomorrow.

In the Church of England, lay leaders voted today to let women become bishops. The measure had the support of the archbishop of Canterbury and of British Prime Minister David Cameron. Two years ago, a similar measure failed to get the required two-thirds majority.

Wall Street got the week off to a strong start. The Dow Jones industrial average gained more than 111 points to close at 17,055. The Nasdaq rose nearly 25 points to close at 4,440. And the S&P 500 added nine, to finish at 1,977.

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